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Unformatted text preview: [1] (b) at least one person receives his or her own hat? [1] (c) exactly one person receives his or her own hat? [1] 3 3. (a) Find a closed form (a.k.a. compact form) of the generating function for the sequence a = 0 and a k = (2) k1 , k ≥ 1 (i.e., 0 , 1 ,2 , 4 ,8 , 16 ,32 , 64 , . . . ) [3] (b) Find the sequence represented by the generating function f ( x ) = x 2 / (1 + x ) 3 . [3] 4 4. Find the generating function for the sequence a n , n ≥ 0, where a n is the number of partitions of n into summands such that (a) each summand is an even number; [2] (b) each summand occurs an odd number of times. [2] 5 5. Find the generating function in a closed form which generates the sequence de±ned by the following recurrence relation (you do not need to solve for it). a n +12 a n = 5 , n ≥ 0; a = 1 . [5]End...
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 Spring '11
 HuangJing
 Math, Recurrence relation, Even and odd functions, Fibonacci number, Generating function, Dr. Jing Huang, Sharp EL510R calculator

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